MHB Who has the advantage in the 1-11 game to reach 56?

[Ackbach]

Here is this week's POTW:

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Two players play the following game. The first player selects any integer from 1 to 11 inclusive. The second player adds any positive integer from 1 to 11 inclusive to the number selected by the first player. They continue in this manner alternately. The player who reaches 56 wins the game. Which player has the advantage?

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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!

 

[Ackbach]

Congratulations to Kiwi, kaliprasad, and Fallen Angel for their correct solutions! Kiwi's solution follows:

Spoiler

Player 1 always wins by following this sequence:

Player 1 plays 8
Player 2 plays 1-11 bringing the total to 9-19
Player 1 brings the total to 20
Player 2 plays 1-11 bringing the total to 21-31
Player 1 brings the total to 32
Player 2 plays 1-11 bringing the total to 33-43
Player 1 brings the total to 44
Player 2 plays 1-11 bringing the total to 45-55
Player 1 brings the total to 56 and wins